FOR 20 years after Harry Truman ordered the atomic bomb dropped on Japan in August 1945, most American scholars and citizens subscribed to the original, official version of the story: the President had acted to avert a horrendous invasion of Japan that could have cost 200,000 to 500,000 American lives. Then a young political economist named Gar Alperovitz published a book of ferocious revisionism, "Atomic Diplomacy: Hiroshima and Potsdam" (1965). While acknowledging the paucity of evidence available at the time, he argued that dropping the atomic bomb "was not needed to end the war or to save lives" but was Truman's means of sending a chastening message to the Soviet Union.

Now, in "The Decision to Use the Atomic Bomb," Mr. Alperovitz, who is the president of the National Center for Economic Alternatives, writes that "oversimplified versions of my argument (together with some obvious graduate-student errors) were pounced upon by critics who could not abide criticism of the Hiroshima decision." Benefiting from documentary discoveries of the past 30 years and the less fractious post-cold war atmosphere, he has produced a more ambitious and far-reaching work. As the author notes, his earlier book focused on "how the bomb influenced diplomacy." With the advantage of greater hindsight and documentation, this volume seeks to deal more comprehensively with the decision to drop the bomb and to suggest why the public clings so tenaciously to the original explanation of why Truman gave the order. With piquant irony, he has chosen the same title that Truman's first Secretary of War, Henry L. Stimson, used in a famous 1947 essay in Harper's that did much to establish the original version of the story in the public mind. Mr. Alperovitz has lost none of his instinct for provocative judgments about one of the century's paramount historical controversies. He has written what will almost certainly serve as a bible for the next generation of revisionist scholars, a book that is elegantly documented (with the aid of seven research collaborators) and intensely argued.

Fifty years after Hiroshima and Nagasaki, Mr. Alperovitz declares that a final answer to why the atomic bomb was used is "neither essential nor possible." He continues with a more debatable premise: "What is important is whether, when the bomb was used, the President and his top advisers understood that it was not required to avoid a long and costly invasion, as they later claimed and as most Americans still believe." More orthodox historical critiques of the atomic bomb decision sometimes question the estimates of casualties to be expected from a full-scale invasion of Japan. The argument goes that if these appraisals were inflated, the President had less business justifying the horror of the bomb as a way of saving lives. This debate is less interesting to Mr. Alperovitz. He insists that without use of the bomb, Japan might still have been made to surrender before the first American landing on the island of Kyushu, planned for November 1945. He notes that many American military leaders then and later felt that using atomic weapons against Japan was unnecessary.

But, Mr. Alperovitz argues, Truman and his Secretary of State, James F. Byrnes, were struck by the notion that ending World War II without dropping the atomic bomb would not have brought added strength to American diplomacy against the Soviet Union in Europe. More than in the earlier book, Byrnes is the villain of this piece. Mr. Alperovitz insists that a decision not to drop the bomb could actually have bolstered American diplomatic objectives in Asia -- for example, by helping to create the atmosphere for a more harmonious postwar American-Soviet relationship. He criticizes Truman for failing to issue a more explicit warning to Japan about the bomb and for attacking Hiroshima rather than a nonurban target, as his Army Chief of Staff, Gen. George C. Marshall, had suggested.

As evidence of the link between the bomb decision and diplomacy toward Moscow, Mr. Alperovitz points to Truman's postponement of his Potsdam meeting with Stalin and Churchill until July 1945, when the new weapon would have been tested. At Potsdam, after hearing about the first successful detonation in New Mexico, Truman turned suddenly more truculent. According to Stimson, Churchill marveled that the President "was a changed man. He told the Russians just where they got on and off and generally bossed the whole meeting." Truman confided to his crony and reparations negotiator Edwin Pauley that the bomb "would keep the Russians straight." Mr. Alperovitz argues that "the U.S. feeling of cheerfulness rather than frustration" over differences with the Soviets at Potsdam "makes little sense unless one realizes that top policy makers were thinking ahead to the time when the force of the new weapon would be displayed."